Subgroups — #23758288

Order 10048.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14578964	C₂	1	1	yes	maximal, characteristic
2	D₁₅₇⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	#19097842	C₂	1	2	yes	maximal, complemented
4	#19097841	C₂	1	2	yes	maximal, complemented
5	M₁₆×D₁₅₇	C₂	1	1	yes	maximal, characteristic
6	#14578964	—	2	1	no	—
7	#14578964	C₂²	1	1	yes	characteristic
8	#14578964	C₂²	1	1	yes	characteristic
9	#14578964	C₂²	1	2	yes	—
10	#14578963	—	2	1	no	—
11	D₁₅₇⋊C₈	—	2	1	no	—
12	C₂×#11929441	—	2	1	no	—
13	C₂×C₄×D₁₅₇	C₂²	1	1	yes	characteristic
14	#14578938	C₄	1	1	yes	characteristic
15	#14578937	C₄	1	2	yes	—
16	C₈×D₁₅₇	C₂²	1	2	yes	—
17	M₁₆×C₁₅₇	C₄	1	1	yes	characteristic
18	#11929441	—	2	2	no	—
19	#11929441	—	2	1	no	—
20	#11929441	—	2	1	no	—
21	C₂²×D₁₅₇	Q₈	1	1	yes	characteristic
22	C₂×Dic₁₅₇	D₄	1	1	yes	characteristic
23	C₄×D₁₅₇	C₂×C₄	1	1	yes	characteristic
24	C₄×D₁₅₇	D₄	1	1	yes	characteristic
25	C₄×D₁₅₇	Q₈	1	1	yes	characteristic
26	C₄×D₁₅₇	C₂³	1	1	yes	characteristic
27	#11929434	C₂×C₄	1	2	yes	—
28	C₂×C₄×C₁₅₇	C₂×C₄	1	1	yes	characteristic
29	C₈×C₁₅₇	C₂×C₄	1	2	yes	—
30	C₂²×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
31	C₂×D₁₅₇	—	4	1	no	—
32	C₂×D₁₅₇	C₄⋊C₄	1	1	yes	characteristic
33	C₂×D₁₅₇	C₂×Q₈	1	1	yes	characteristic
34	C₄×C₁₅₇	C₄⋊C₄	1	1	yes	characteristic
35	C₄×C₁₅₇	C₂²×C₄	1	1	yes	characteristic
36	Dic₁₅₇	C₄⋊C₄	1	1	yes	characteristic
37	Dic₁₅₇	C₂×D₄	1	1	yes	characteristic
38	C₂×C₁₅₇	—	2	1	no	—
39	C₂×C₁₅₇	C₂×C₄⋊C₄	1	1	yes	characteristic
40	D₁₅₇	—	2	1	no	—
41	D₁₅₇	—	2	1	no	—
42	C₁₅₇	#430	1	1	yes	characteristic, complemented, Sylow
43	#430	—	157	1	no	maximal, Sylow
44	C₂×M₁₆	—	157	1	no	—
45	C₂×M₁₆	—	157	1	no	—
46	C₂×M₁₆	—	157	1	no	—
47	#108	—	157	2	no	—
48	#108	—	157	2	no	—
49	C₂²×C₄	—	157	1	no	—
50	M₁₆	—	314	1	no	—
51	M₁₆	—	314	1	no	—
52	M₁₆	—	157	1	no	—
53	M₁₆	—	157	1	no	—
54	M₁₆	—	157	2	no	—
55	M₁₆	—	157	1	no	—
56	M₁₆	—	157	2	no	—
57	M₁₆	#10597845	1	1	yes	characteristic
58	C₂×C₈	—	314	1	no	—
59	C₂×C₈	—	314	1	no	—
60	C₂×C₈	—	157	2	no	—
61	C₂³	—	157	1	no	—
62	C₂×C₄	—	157	1	no	—
63	C₂×C₄	—	157	1	no	—
64	C₂×C₄	—	157	1	no	—
65	C₂×C₄	—	157	1	no	—
66	C₂×C₄	—	157	1	no	—
67	C₂×C₄	C₂×#10597845	1	1	yes	characteristic
68	C₈	—	314	2	no	—
69	C₈	—	314	1	no	—
70	C₈	—	314	1	no	—
71	C₈	—	157	2	no	—
72	C₈	C₂×#10597845	1	2	yes	—
73	C₂²	—	628	1	no	—
74	C₂²	—	157	1	no	—
75	C₂²	—	157	1	no	—
76	C₂²	C₄⋊#10597845	1	1	yes	characteristic
77	C₄	—	157	1	no	—
78	C₄	—	157	1	no	—
79	C₄	C₄⋊#10597845	1	1	yes	characteristic
80	C₄	C₂²×#10597845	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	—	314	1	no	—
83	C₂	—	314	1	no	—
84	C₂	C₂×C₄⋊#10597845	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₄⋊#10597845
commutator	C₄×C₁₅₇	C₂²×C₄
Frattini	C₄	C₂²×#10597845
Fitting	M₁₆×C₁₅₇	C₄
socle	C₂×C₁₅₇	C₂×C₄⋊C₄
prime radical	C₂²×D₁₅₇	Q₈
cosocle	C₄×D₁₅₇	C₂³
hypercenter	M₁₆	#10597845
hypocenter	C₁₅₇	#430
LCS	G ▷ C₄×C₁₅₇ ▷ C₂×C₁₅₇ ▷ C₁₅₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #19097842	C₂	semidirect
4. #19097841	C₂	semidirect
42. C₁₅₇	#430	semidirect